DO NOT let your car get taken; that's ridiculous. I would try to trade it in for something with lower payments though. Public transportation is not as developed here, so I'd be loathe to be without a car in case someone gets a job when or where the bus doesn't go.
Someone else suggested it, and I second the idea because it's what I personally did at one time: we needed extra money and I got a job at a daycare. Some lower the rates for employees....I even worked part time at one daycare, and my son only attended during the hours I worked, so he was free. I made just about $150/week for part time, which isn't much, but it's a lot when you don't have anything coming in!
Remember that honesty is best, but there's also a weight that children shouldn't have to bear. Imagine that information and responsibility are things that you put in your backpack to carry on your journey: younger children have smaller packs, and need to carry smaller loads. You could say the family is going through a bumpy time and have to be careful with things, but you're together and love each other and that's more than a lot of people have. Where you live will change from time to time, but being here for each other and loving each other won't change. You could even tell her that you're looking for jobs and need to save money for your own place. Anything more than that is too much weight for a little one.
Seven years ago, I had a life changing experience: I was alone and driving in another state, about 20 minutes from where I lived as a toddler. I thought "I'm gonna find that place" and drove straight to it....a low income apartment community where my divorced mom and I lived in the 70s. Mom didn't seek childsupport (we were hiding from my dad), we didn't have assistance from the government, the only assistance we actually had was childcare---I stayed at my grandma's house when mom was at work. I found the exact building I lived in, and sat in my car watching the stoop. I took a napkin and wrote down everything I remembered about the place on the inside (slope on the floor by the door, colors, style of doorknob, how many doors are inside, what the stairs looked like, etc). I walked in, and was right about every single detail! I told mom about it, because it was the safest, happiest time in my childhood memory, even though she went on and married a nice man who adopted me and we lived in upper middleclass my whole life after I was 4 years old. When I told my mom, she cried bitterly and said it was the roughest, scariest, most unsure time of her life. We had NOTHING, stayed in a 1 bedroom converted officer's barracks, she shared a can of spaghetti o's with me for dinner, we were very very poor. She had "mom guilt" because she worked 40+ hours/week. She couldn't believe my memory was so different.
That long story to say this: I remembered that mom was there, that we were a TEAM, she sang songs to me and told me stories, I lived in a place that was clean and felt safe, and I knew I was loved. The things we parents strive so hard to give our children, I grew up with later...but they didn't make the same impression on me. It forever changed the way I lived and influenced the manner in which I raise my own son (and another on the way!). The little things really are what matter, and they really are things that cost little to no money.
I would suggest that you don't go buy a bunch of junk in a dollar store that you have to keep with you and clutter up stuff since you may be moving around a little while til things change (and they will change). I would totally suggest doing something you've never done before and get creative (I like that Dora map idea someone had, but make little notes or treats instead of trinkets, and then the treasure be her gift), or go to a free thing like a spraypark/park/playground, we LOVE the botanical gardens, and it's free everywhere but the Japanese garden...bring a picnic and cupcakes or make a box cake. Do the candles and sing to her, have some friends there for that if you can. Half price bookstore for books/crafts, a thrift store for a toy, those are options for a gift. What would SHE like as far as doing something fun? Do an activity or spend the day somewhere. But if the day is all about her, it doesn't have to be all about a gift.